Quantum Duality Maps, Skein Algebras and their Ensemble Compatibility
We generalize the quantum duality map I A of Allegretti–Kim (Adv Math 306:1164–1208, 2017) for punctured closed surfaces to general marked surfaces. When the marked surface has no interior marked points, we investigate its compatibility with the quantum duality map I X on the dual side based on the...
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| creator | Ishibashi, Tsukasa Karuo, Hiroaki |
| description | We generalize the quantum duality map
I
A
of Allegretti–Kim (Adv Math 306:1164–1208, 2017) for punctured closed surfaces to general marked surfaces. When the marked surface has no interior marked points, we investigate its compatibility with the quantum duality map
I
X
on the dual side based on the quantum bracelets basis (Mandel and Qin in
arXiv:2301.11101
; Thurston in Proc Natl Acad Sci USA 111(27):9725–9732, 2014). Our construction factors through reduced stated skein algebras, based on the quantum trace maps (Lê in Quantum Topol 9(3):591–632, 2018) together with an appropriate way of
skein lifting
of integral
A
-laminations. We also give skein theoretic proofs for some expected properties of Laurent expressions, and positivity of structure constants for marked disks and a marked annulus. |
| doi_str_mv | 10.1007/s00220-024-05119-y |
| format | Article |
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I
A
of Allegretti–Kim (Adv Math 306:1164–1208, 2017) for punctured closed surfaces to general marked surfaces. When the marked surface has no interior marked points, we investigate its compatibility with the quantum duality map
I
X
on the dual side based on the quantum bracelets basis (Mandel and Qin in
arXiv:2301.11101
; Thurston in Proc Natl Acad Sci USA 111(27):9725–9732, 2014). Our construction factors through reduced stated skein algebras, based on the quantum trace maps (Lê in Quantum Topol 9(3):591–632, 2018) together with an appropriate way of
skein lifting
of integral
A
-laminations. We also give skein theoretic proofs for some expected properties of Laurent expressions, and positivity of structure constants for marked disks and a marked annulus.</description><identifier>ISSN: 0010-3616</identifier><identifier>EISSN: 1432-0916</identifier><identifier>DOI: 10.1007/s00220-024-05119-y</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Classical and Quantum Gravitation ; Compatibility ; Complex Systems ; Mathematical and Computational Physics ; Mathematical Physics ; Physics ; Physics and Astronomy ; Quantum Physics ; Relativity Theory ; Skeins ; Theoretical</subject><ispartof>Communications in mathematical physics, 2024-10, Vol.405 (10), Article 244</ispartof><rights>The Author(s) 2024</rights><rights>The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c244t-fb4a6e6462dedadd1950dbc3e118eeacd4708af7924a01803225ffcd1e5198393</cites><orcidid>0000-0002-6982-189X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00220-024-05119-y$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00220-024-05119-y$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Ishibashi, Tsukasa</creatorcontrib><creatorcontrib>Karuo, Hiroaki</creatorcontrib><title>Quantum Duality Maps, Skein Algebras and their Ensemble Compatibility</title><title>Communications in mathematical physics</title><addtitle>Commun. Math. Phys</addtitle><description>We generalize the quantum duality map
I
A
of Allegretti–Kim (Adv Math 306:1164–1208, 2017) for punctured closed surfaces to general marked surfaces. When the marked surface has no interior marked points, we investigate its compatibility with the quantum duality map
I
X
on the dual side based on the quantum bracelets basis (Mandel and Qin in
arXiv:2301.11101
; Thurston in Proc Natl Acad Sci USA 111(27):9725–9732, 2014). Our construction factors through reduced stated skein algebras, based on the quantum trace maps (Lê in Quantum Topol 9(3):591–632, 2018) together with an appropriate way of
skein lifting
of integral
A
-laminations. We also give skein theoretic proofs for some expected properties of Laurent expressions, and positivity of structure constants for marked disks and a marked annulus.</description><subject>Classical and Quantum Gravitation</subject><subject>Compatibility</subject><subject>Complex Systems</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Physics</subject><subject>Relativity Theory</subject><subject>Skeins</subject><subject>Theoretical</subject><issn>0010-3616</issn><issn>1432-0916</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kEtLxDAURoMoOI7-AVcBt0bvTdK0XQ7j-ABFRF2HtEnHjn2ZtIv-eztWcOfqbs75LhxCzhGuECC-DgCcAwMuGUSIKRsPyAKl4AxSVIdkAYDAhEJ1TE5C2AFAypVakM3LYJp-qOnNYKqyH-mT6cIlff10ZUNX1dZl3gRqGkv7D1d6ummCq7PK0XVbd6Yvs3JvnZKjwlTBnf3eJXm_3byt79nj893DevXIci5lz4pMGuWUVNw6a6zFNAKb5cIhJs6Z3MoYElPEKZcGMAHBeVQUuUUXYZqIVCzJxbzb-fZrcKHXu3bwzfRSC0SJk8DjieIzlfs2BO8K3fmyNn7UCHqfS8-59JRL_-TS4ySJWQoT3Gyd_5v-x_oGcEZtXw</recordid><startdate>20241001</startdate><enddate>20241001</enddate><creator>Ishibashi, Tsukasa</creator><creator>Karuo, Hiroaki</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-6982-189X</orcidid></search><sort><creationdate>20241001</creationdate><title>Quantum Duality Maps, Skein Algebras and their Ensemble Compatibility</title><author>Ishibashi, Tsukasa ; Karuo, Hiroaki</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c244t-fb4a6e6462dedadd1950dbc3e118eeacd4708af7924a01803225ffcd1e5198393</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Classical and Quantum Gravitation</topic><topic>Compatibility</topic><topic>Complex Systems</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Physics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Physics</topic><topic>Relativity Theory</topic><topic>Skeins</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ishibashi, Tsukasa</creatorcontrib><creatorcontrib>Karuo, Hiroaki</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Communications in mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ishibashi, Tsukasa</au><au>Karuo, Hiroaki</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Quantum Duality Maps, Skein Algebras and their Ensemble Compatibility</atitle><jtitle>Communications in mathematical physics</jtitle><stitle>Commun. Math. Phys</stitle><date>2024-10-01</date><risdate>2024</risdate><volume>405</volume><issue>10</issue><artnum>244</artnum><issn>0010-3616</issn><eissn>1432-0916</eissn><abstract>We generalize the quantum duality map
I
A
of Allegretti–Kim (Adv Math 306:1164–1208, 2017) for punctured closed surfaces to general marked surfaces. When the marked surface has no interior marked points, we investigate its compatibility with the quantum duality map
I
X
on the dual side based on the quantum bracelets basis (Mandel and Qin in
arXiv:2301.11101
; Thurston in Proc Natl Acad Sci USA 111(27):9725–9732, 2014). Our construction factors through reduced stated skein algebras, based on the quantum trace maps (Lê in Quantum Topol 9(3):591–632, 2018) together with an appropriate way of
skein lifting
of integral
A
-laminations. We also give skein theoretic proofs for some expected properties of Laurent expressions, and positivity of structure constants for marked disks and a marked annulus.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00220-024-05119-y</doi><orcidid>https://orcid.org/0000-0002-6982-189X</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Classical and Quantum Gravitation Compatibility Complex Systems Mathematical and Computational Physics Mathematical Physics Physics Physics and Astronomy Quantum Physics Relativity Theory Skeins Theoretical |
| title | Quantum Duality Maps, Skein Algebras and their Ensemble Compatibility |
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